Question

If G (-4,7) is the centroid of the triangle ABC where A(-1,-7),B(3,5). Find the coordinates of C

Answer 1

Answer:

${\bold{\therefore Coordinate\:of\:C=(-14,23)}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about a triangle whose two coordinate of vertices is given and coordinate of centroid of triangle is given.

• We have to find the third coordinate.

$\underline \bold{Given :} \\ \implies Coordinate \: of \: A = ( - 1,- 7) \\ \implies Coordinte \: of \: B = (3,5) \\ \implies Centroid(G) = ( - 4,7)\\\underline\bold{To\:Find:}\\\implies Coordinate\:of\:C=(x_{3},y_{3})$

• According to the given question :

$\bold{By \: centroid \: formula : } \\ \bold{For \: x \:abscissa}\\ \implies x = \frac{ x_{1} + x_{2} +x_{3}}{3} \\ \implies - 4 = \frac{ - 1 + 3 + x_{3} }{3} \\ \implies - 4 \times 3 = 2 + x_{3} \\ \implies - 12 - 2 = x_{3} \\ \bold{\implies x_{3} = - 14} \\ \\ \bold{For \: y \: ordinate : } \\ \implies y = \frac{y_{1} +y_{2} +y_{3}}{3} \\ \implies 7 = \frac{ - 7 +5 + y_{3}}{3} \\ \implies 7 \times 3 = - 2 + y_{ 3} \\ \implies 21 = - 2 + y_{3} \\ \implies y_{ 3} = 21 + 2 \\ \bold{\implies y_{3} = 23} \\ \\ \bold{ \therefore Coordinate \: of \: C= (-14,23)}$

Answer 2

ANSWER:-

Given:

If G(-4,7) is the centroid of the ∆ABC, where A(-1,-7), B(3,5).

To find:

Find the coordinates of C.

Solution:

We know that, coordinates of the centroid;

$= > (\frac{x1 + x2 + x3}{3} ,\: \frac{y1 + y2 + y3}{3} )$

Therefore,

Two vertices of ∆ABC. [given]

⏺️A(-1,-7)

⏺️B(3,5)

Let C(a,b) be the third vertices of ∆ABC.

Therefore,

The coordinates of its centroid are;

$G( \frac{ - 1 + 3 + a}{3} , \frac{ - 7 + 5 + b}{ 3} ) \\ \\ = > G( \frac{2 + a}{3} , \frac{ - 2 + b}{ 3} )$

Given that,

The centroid is G(-4,7).

$= > \frac{2 + a}{3} = - 4 \: \: \: and \: \: \: \frac{ - 2 + b}{3} = 7 \\ \\ = > 2 + a = - 12 \: \: \: and \: \: \: - 2 + b = 21 \\ \\ = > a = - 12 - 2 \: \: \: and \: \: b = 21 + 2 \\ \\ = > a = - 14 \: \: \: and \: \: \: b = 23$

Hence,

C(-14, 23) is the third vertex of ∆ABC.

Hope it helps ☺️